A Windows based mathematical graphing tool for 2D and 3D Functions and Data, shaded surfaces, contour plots. Includes linear and nonlinear curve fitting. You may integrate and analyse systems of up to 20 coupled ordinary differential equations (ODE's). Analysis tools include power spectrum calculation and Poincare sections. You may use these tools to study chaos in dynamical systems.
Mathematical graphing tool for 2D and 3D functions and data. Includes nonlinear curve fitting and integration of coupled ordinary differential equations (ODE's). Study chaos in dynamical systems.
MathGrapher ranks between graphical calculators and full-fledged mathematical tools like Mathematica.
It is powerful, easy to use and will probably meet your demands for a price that consists of only 2 instead of 4 digits.
Mathgrapher version 2 has just been released. You are invited to download a fully functional trial version.
Install Mathgrapher, start the Demonstrations and see what Mathgrapher can do for you.
Functions in 2D and 3D
MathGrapher is a graphical calculator for functions of the form F(x) and F(x,y)
containing up to 20 subfunctions and 150 numerical and 100 named constants. Cartesian as well as polar coordinates can be
chosen and functions can be represented in patametrized form (2D). F(x,y) can be represented in 2D and 3D
by Shaded surfaces, Contour plots and Cross-sections through Contourplots. In the 3D viewer you may rapidly vary the
viewing angle, distance and shading of the 3D surface using your mouse.
Data in 2D and 3D
Edit and draw graphs of your 2D or 3D Data. 3D surfaces can be previewed in the 3D viewer (OpenGL). Shaded surfaces,
Contour plots and Cross-sections through Contour plots can be drawn in same way as 3D Functions.
Curve fitting (linear and non-linear)
A number of least squares curve fitting methods can be selected: e.g. linear regression, polynomials, trigonometric
polynomials and cubic splines. An important feature of this program is that you can use the
general and powerfull (non-linear) Levenberg-Marquardt method to fit your data to any continuous function you define.
Calculate algebraic series or study iterative multi-dimensional maps. Several mathematical tools are
available to analyse the results (zie ODE's below). Look at the examples to see how you may use Mathgrapher to
study the route to chaos via period doublings in the simple logistic map
Ordinary Differential Equations (ODE's)
The evolution of dynamical systems in physics, chemistry, electronics, economics and population dynamics can often
be described with a set of coupled ODE's. Mathgrapher uses an
accurate Adams-Bashforth variable order, variable step predictor-corrector algorithm to
integrate systems of up to 20 coupled ODE's. Several tools are available to analyse the
results of the integrations (and iterations) such as: Graph of the time evolution,
Projections in 2 or 3 dimensions, Surfaces of Section and Power spectrum analysis.
You are here: Modules > Iterations
Links in the text refer to the lower part of the page
A special window has been added in Mathgrapher v2 to allow detailed presentation
of 2D orbits at the pixel level and to study the stability of the orbits (see the Examples and Demonstrations for the Henon map, Standard map and Mandelbrot and Julia sets.
such as e = 1+ 1/2! + 1/3! + ..., a square wave,
Study iterative maps, e.g. the (one-dimensional)
(see below) or more complicated multi-dimensional maps. The logistic map is perhaps one of the simples mathematical system showing many characteristics
of the development of
Several analytical tools
are valailable to study the results of Iterations and ODE's such as:
Projection in 2D
applied to the logistic map:
Choose a pair of F's from the Functions that are iterated and push Draw to make a
graph where the X-axis represents the first and the Y-axis the second Function.
The example below is a graph of F1 and F2 for a series of 1024 iterations of the logistic map.
The first 100 iterations are omitted. Note that a 4-cycle has developed for a=0.87.
Same as above for a=0.89 showing an 8-cycle and a=0.96 (the gap in the bifurcation diagram)
where we have a 3-cycle. The behaviour is chaotic above 0.96.